evaluate the table and find d/dx [g[f(2x)]] at x=1

Question

f(x) 6,1,6,2
f'(x) 1,2,5,7
g(x) 1,4,4,3
g'(x) 4,5,5,-4

Answer 1

Assuming the x values for the table are 1,2,3,4 then

d/dx g(f(2x))
= g'(f(2x)) * f'(2x) * 2
= g'(f(2)) * f'(2) * 2
= g'(1) * 2 * 2
= 5*2*2
= 20

consider something like y = e^sin(2x)
y'(x) = e^sin(2x) * cos(2x) * 2